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 A052217 Numbers whose sum of digits is 3. 43
 3, 12, 21, 30, 102, 111, 120, 201, 210, 300, 1002, 1011, 1020, 1101, 1110, 1200, 2001, 2010, 2100, 3000, 10002, 10011, 10020, 10101, 10110, 10200, 11001, 11010, 11100, 12000, 20001, 20010, 20100, 21000, 30000, 100002, 100011, 100020, 100101 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS From Joshua S.M. Weiner, Oct 19 2012: (Start) Sequence is a representation of the "energy states" of "multiplex" notation of 3 quantum of objects in a juggling pattern. 0 = an empty site, or empty hand. 1 = one object resides in the site. 2 = two objects reside in the site. 3 = three objects reside in the site. (See A038447.) (End) A007953(a(n)) = 3; number of repdigits = #{3,111} = A242627(3) = 2. - Reinhard Zumkeller, Jul 17 2014 Can be seen as a table whose n-th row holds the n-digit terms {10^(n-1) + 10^m + 10^k, 0 <= k <= m < n}, n >= 1. Row lengths are then (1, 3, 6, 10, ...) = n*(n+1)/2 = A000217(n). The first and the n last terms of row n are 10^(n-1) + 2 resp. 2*10^(n-1) + 10^k, 0 <= k < n. - M. F. Hasler, Feb 19 2020 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..10000 (terms 1..84 from Vincenzo Librandi, terms 85..1140 from T. D. Noe) FORMULA T(n,k) = 10^(n-1) + 10^A003056(k) + 10^A002262(k) when read as a table with row lengths n*(n+1)/2, n >= 1, 0 <= k < n*(n+1)/2. - M. F. Hasler, Feb 19 2020 a(n) = 10^A056556(n-1) + 10^A056557(n-1) + 10^A056558(n-1). - Kevin Ryde, Apr 17 2021 MATHEMATICA Union[FromDigits/@Select[Flatten[Table[Tuples[Range[0, 3], n], {n, 6}], 1], Total[#]==3&]] (* Harvey P. Dale, Oct 20 2012 *) Select[Range[10^6], Total[IntegerDigits[#]] == 3 &] (* Vincenzo Librandi, Mar 07 2013 *) Union[Flatten[Table[FromDigits /@ Permutations[PadRight[s, 18]], {s, IntegerPartitions[3]}]]] (* T. D. Noe, Mar 08 2013 *) PROG (Magma) [n: n in [1..100101] | &+Intseq(n) eq 3 ]; // Vincenzo Librandi, Mar 07 2013 (Haskell) a052217 n = a052217_list !! (n-1) a052217_list = filter ((== 3) . a007953) [0..] -- Reinhard Zumkeller, Jul 17 2014 (PARI) isok(n) = sumdigits(n) == 3; \\ Michel Marcus, Dec 28 2015 (PARI) apply( {A052217_row(n, s, t=-1)=vector(n*(n+1)\2, k, t++>s&&t=!s++; 10^(n-1)+10^s+10^t)}, [1..5]) \\ M. F. Hasler, Feb 19 2020 (Python) from itertools import count, islice def agen(): yield from (10**i + 10**j + 10**k for i in count(0) for j in range(i+1) for k in range(j+1)) print(list(islice(agen(), 40))) # Michael S. Branicky, May 14 2022 CROSSREFS Cf. A069521 to A069530, A069532 to A069537. Cf. A007953, A218043 (subsequence). Row n=3 of A245062. Other digit sums: A011557 (1), A052216 (2), A052218 (4), A052219 (5), A052220 (6), A052221 (7), A052222 (8), A052223 (9), A052224 (10), A166311 (11), A235151 (12), A143164 (13), A235225(14), A235226 (15), A235227 (16), A166370 (17), A235228 (18), A166459 (19), A235229 (20). Other bases: A014311 (binary), A226636 (ternary), A179243 (Zeckendorf). Cf. A242614, A242627. Cf. A003056, A002262 (triangular coordinates), A056556, A056557, A056558 (tetrahedral coordinates). Sequence in context: A017197 A051369 A069538 * A119507 A044436 A210282 Adjacent sequences: A052214 A052215 A052216 * A052218 A052219 A052220 KEYWORD base,easy,nonn AUTHOR Henry Bottomley, Feb 01 2000 EXTENSIONS Offset changed from 0 to 1 by Vincenzo Librandi, Mar 07 2013 STATUS approved

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Last modified May 19 14:45 EDT 2024. Contains 372698 sequences. (Running on oeis4.)